use an inverse trig function to write theta as a function of x
(There is a right triangle drawn.
The hypotenuse is 2.
Theta is the angle between the base and the hypotenuse.
The base/adjacent side of theta is labeled(x + 1)
The side opposite theta does not have a value.)
Use an inverse trig function to write theta as a function of x:
a) theta = sqrt [4 - (x + 1)^2] all divided by 2
b)theta = arccos [(x + 1)/2]
c)theta = arctan[(x + 1)/2]
d)theta = arcsin [2/(x + 1)]
How do I do this? I'm leaning towards B, the inverse cosine because only the adjacent side and hypotenuse are given. The opposite side is not given, and there is already a variable x in the given adjacent side.
Am I on the right track? If not, please explain. Thank you.
find sin 20,cos 20 and tan 20 given that cos 0<=-4/5 and 90 degrees<0<180 degrees
Yes, you are on the right track! The most appropriate inverse trig function to use in this case is indeed the arccosine (arccos), which corresponds to option (b).
The arccosine function allows us to find the angle whose adjacent side length is given as a ratio of the hypotenuse. In this case, the adjacent side is (x + 1) and the hypotenuse is 2. So, the formula theta = arccos[(x + 1)/2] allows us to express theta as a function of x.
Therefore, option (b) is the correct choice for expressing theta as a function of x. Well done!
Yes, you are on the right track. To determine the correct inverse trig function to use, we need to identify which sides of the triangle are given. In this case, you correctly noted that only the adjacent side and the hypotenuse are given.
When the adjacent side and the hypotenuse are given, we can use the inverse cosine function (arccos) to write theta as a function of x.
To apply the inverse cosine function, we need to use the ratio of the adjacent side and the hypotenuse. In this triangle, it is given as (x + 1)/2. Therefore, the correct equation is:
theta = arccos [(x + 1)/2]
Thus, the correct answer is b) theta = arccos [(x + 1)/2].
Well done!
Leaning? Lord, solve the triangle.
so cosine Theta=(x+1)/2
So lean on B.